Spacecraft Charging Due To Energetic Electrons and Ions at Geosynchronous Altitudes

Abstract

Satellites and spacecraft are usually exposed to space plasma disturbances, which vary in time at Geosynchronous Earth Orbit (GEO), affecting the charging of spacecraft and weather on the Earth. The charging currents are often described by the current‐balance equation (CBE) containing the electron‐ion (incoming/outgoing) current density fluxes and their energy distributions. The power‐law q‐distribution is the most generalized distribution that essentially characterizes more pronounced energy tails and can be reduced to standard Maxwellian distribution for q → 1. Using the equilibrium currents, the CBE is solved both analytically and numerically to study spacecraft charging within the framework of Whittaker function. It is found that energetic electron and ion‐induced currents significantly modify the charging phenomenon on the spacecraft's surface. Especially, ion‐induced currents result in the delay of negative charging at critical electron thermal energy and enhance the magnitude of the total normalized current. Apart from CuBe surface material, numerical analysis is also carried out for silver and Aluminum to determine the magnitude of total normalized current and onset of negative charging. The present findings are consistent with spacecraft charging at GEO altitudes around the Earth.

Numerical Calculations of Charging Threshold at GEO Altitudes With Two Temperature Non‐Extensive Electrons

“…Here, <δ + η> c,h is the average secondary and back-scattered electron yield for two plasma components T c and T h whose values are now dependent on the non-extensive q − parameter given by, The modified threshold condition Equation 12, is the weighted average over the total secondary and back-scattered electron yields and equals to unity 𝐴𝐴 < 𝛿𝛿 + 𝜂𝜂 𝜂𝑐𝑐𝑐𝑐 = 1 , accounted by the two-temperature q − non-extensive energy distribution function. The current balance equation is developed with the help of the Whittaker function which is commonly used to describe charging related problems (Harris, 2003;Morse & Feshbach, 1953;Pervaiz et al, 2023). Equation 12is valid for spacecraft charging in eclipse and in the limit T h = 0, we obtain the expression for the single temperature q − non-extensive case (Ali et al, 2020), that is,…”

“…The modified threshold condition Equation , is the weighted average over the total secondary and back‐scattered electron yields and equals to unity $$\overline{< \delta +{\eta > }_{c,h}}=1$$, accounted by the two‐temperature q − non‐extensive energy distribution function. The current balance equation is developed with the help of the Whittaker function which is commonly used to describe charging related problems (Harris, 2003; Morse & Feshbach, 1953; Pervaiz et al., 2023). Equation is valid for spacecraft charging in eclipse and in the limit T h = 0, we obtain the expression for the single temperature q − non‐extensive case (Ali et al., 2020), that is, $$$\frac{2{q}^{2}-q}{1-q}\left\{c{U}_{1}-c{U}_{2}-B{U}_{3}\right\}+A-1=0.$$$ …”

“…It was revealed that the kappa distribution better explains the super‐thermal charge particles but in the case of low‐level charging, the kappa distribution has no significant benefit over Maxwellian. A number of authors have explained that the particle velocity distribution function is often non‐Maxwellian (Livadiotis & McComas, 2013) and have successfully employed different approaches such as q − non‐extensive distribution (Ali et al., 2020; Pervaiz et al., 2023). The q − non‐extensive distribution is better than the kappa distribution as it captures the high energy tail along with the effects of long‐range interparticle forces for example, Coulomb forces.…”

“…During an eclipse at GEO orbit, the ambient electron current contributes to negative spacecraft potential, particularly when geomagnetic storms and substorms are enhancing the electron flux. On the other hand, when spacecraft are exposed to sunlight the emission of photo‐electrons leads to positive charging of a few volts under very low density and temperature conditions which are not usually found in GEO (Pervaiz et al., 2023). A high‐level negative charging was also observed in sunlight due to the differential charge, which acts as a potential barrier between surfaces and prevents photo‐electrons from escaping on the sunlit side, but to form the barriers to sunlight charging the ambient electron temperature or flux should be very high (Ferguson et al., 2015; Huang et al., 2017).…”